Electric Circuits Legacy Problem #8 Guided Solution
Problem*
Defibrillator machines are used to deliver an electric shock to the human heart in order to resuscitate an otherwise non-beating heart. It is estimated that a current as low as 17 mA through the heart is required to resuscitate. Using 100,000 Ω as the overall resistance, determine the output voltage required of a defibrillating device.
Audio Guided Solution
In mechanics, F net equal m a is the big equation. In an electric circuitry, delta V equal I times R is of similar nature. The electric potential difference between two points is equal to the product of the current multiplied by the resistance. That is, delta V in units of volts is equal to I current in units of amperes multiplied by R in units of ohms. And so, here in this problem, we have to calculate the electric potential difference or output voltage of a defibrillating device knowing that the current needs to be as high as 17 milliamps and knowing that the general resistance of a human heart is about 100,000 ohms. So, one of the first things we need to do is to take out 17 milliamps and convert it to units of amps. Now, there are 1,000 milliamps per one ampere and so we can move the decimal place three places such that the current, I, is equal to 0.017 amperes. We can multiply that by the resistance of 100,000 ohms and when we do, we end up getting the delta V, or output voltage, across the device. It comes out to be 1,700 volts or about 2,000 volts.
Solution
1700 V
Habbits of an Effective Problem Solver
- Read the problem carefully and develop a mental picture of the physical situation. If necessary, sketch a simple diagram of the physical situation to help you visualize it.
- Identify the known and unknown quantities and record them in an organized manner. Equate given values to the symbols used to represent the corresponding quantity - e.g., \(\descriptive{\text{δV}}{δV,change in voltage} = 9.0\unit{\volt}\); \(\descriptive{R}{R,resistance} = 0.025\unit{\ohm}\); \(\descriptive{I}{I,current} = \colorbox{gray}{Unknown}\).
- Use physics formulas and conceptual reasoning to plot a strategy for solving for the unknown quantity.
- Identify the appropriate formula(s) to use.
- Perform substitutions and algebraic manipulations in order to solve for the unknown quantity.
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